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Dependence in Probability and Statistics [Pehme köide]

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  • Formaat: Paperback / softback, 205 pages, kõrgus x laius: 235x155 mm, kaal: 720 g, 13 Illustrations, black and white; XV, 205 p. 13 illus., 1 Paperback / softback
  • Sari: Lecture Notes in Statistics 200
  • Ilmumisaeg: 11-Aug-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 364214103X
  • ISBN-13: 9783642141034
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Dependence in Probability and StatisticsSuurem pilt
  • Formaat: Paperback / softback, 205 pages, kõrgus x laius: 235x155 mm, kaal: 720 g, 13 Illustrations, black and white; XV, 205 p. 13 illus., 1 Paperback / softback
  • Sari: Lecture Notes in Statistics 200
  • Ilmumisaeg: 11-Aug-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 364214103X
  • ISBN-13: 9783642141034
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783642141034.html
Märksõnad:
This volume contains several contributions on the general theme of dependence for several classes of stochastic processes, andits implicationson asymptoticproperties of various statistics and on statistical inference issues in statistics and econometrics. The chapter by Berkes, Horvath and Schauer is a survey on their recent results on bootstrap and permutation statistics when the negligibility condition of classical central limit theory is not satis ed. These results are of interest for describing the asymptotic properties of bootstrap and permutation statistics in case of in nite va- ances, and for applications to statistical inference, e.g., the change-point problem. The paper by Stoev reviews some recent results by the author on ergodicity of max-stable processes. Max-stable processes play a central role in the modeling of extreme value phenomena and appear as limits of component-wise maxima. At the presenttime,arathercompleteandinterestingpictureofthedependencestructureof max-stable processes has emerged,involvingspectral functions, extremalstochastic integrals, mixed moving maxima, and other analytic and probabilistic tools. For statistical applications, the problem of ergodicity or non-ergodicity is of primary importance.
Permutation and bootstrap statistics under infinite variance
1(20)
Istvan Berkes
Lajos Horvath
Johannes Schauer
1 Introduction
1(1)
2 Some general sampling theorems
2(8)
3 Application to change point detection
10(9)
References
19(2)
Max-Stable Processes: Representations, Ergodic Properties and Statistical Applications
21(22)
Stilian A. Stoev
1 Introduction
21(3)
2 Representations of Max-Stable Processes
24(5)
3 Ergodic Properties of Stationary Max-stable Processes
29(3)
4 Examples and Statistical Applications
32(8)
4.1 Ergodic Properties of Some Max-Stable Processes
32(3)
4.2 Estimation of the Extremal Index
35(5)
References
40(3)
Best attainable rates of convergence for the estimation of the memory parameter
43(16)
Philippe Soulier
1 Introduction
43(2)
2 Lower bound
45(2)
3 Upper bound
47(2)
4 Bandwidth selection
49(2)
5 Technical results
51(5)
References
56(3)
Harmonic analysis tools for statistical inference in the spectral domain
59(12)
Florin Avram
Nikolai Leonenko
Ludmila Sakhno
1 Introduction
59(2)
2 Motivation
61(3)
3 Main result
64(3)
4 Applications and discussion
67(3)
References
70(1)
On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time
71(32)
Beatrice Vedel
Herwig Wendt
Patrice Abry
Stephane Jaffard
1 Motivation
72(2)
2 Infinitely divisible processes
74(4)
2.1 Infinitely divisible cascade
74(2)
2.2 Infinitely divisible motion
76(2)
2.3 Fractional Brownian motion in multifractal time
78(1)
3 Multiresolution quantities and scaling parameter estimation
78(2)
3.1 Multiresolution quantities
78(2)
3.2 Scaling parameter estimation procedures
80(1)
4 Dependence structures of the multiresolution coefficients: analytical study
80(5)
4.1 Correlation structures for increment and wavelet coefficients
81(2)
4.2 Higher order correlations for increments
83(2)
4.3 Role of the order of the increments
85(1)
5 Dependence structures of the multiresolution coefficients: Conjectures and numerical studies
85(4)
5.1 Conjectures
85(1)
5.2 Numerical simulations
86(3)
6 Discussions and conclusions on the role of the number of vanishing moments
89(1)
7 Proofs
90(9)
7.1 A key lemma
90(1)
7.2 Proof of Theorem 4.1
91(2)
7.3 Proof of Theorem 4.2
93(1)
7.4 Proof of Proposition 0.6
94(1)
7.5 Proof of Proposition 0.7
95(4)
7.6 Proof of Proposition 0.8
99(1)
References
99(4)
Multifractal scenarios for products of geometric Ornstein-Uhlenbeck type processes
103(20)
Vo V. Anh
Nikolai N. Leonenko
Narn-Rueih Shieh
1 Introduction
103(1)
2 Multifractal products of stochastic processes
104(4)
3 Geometric Ornstein-Uhlenbeck processes
108(5)
4 Multifractal Ornstein-Uhlenbeck processes
113(7)
4.1 Log-tempered stable scenario
113(3)
4.2 Log-normal tempered stable scenario
116(4)
References
120(3)
A new look at measuring dependence
123(20)
Wei Biao Wu
Jan Mielniczuk
1 Introduction
123(2)
2 Bivariate dependence
125(8)
2.1 Global dependence measures
126(4)
2.2 Local dependence measures
130(3)
3 Connections with reliability theory
133(2)
4 Multivariate dependence
135(2)
5 Moment inequalities and limit theorems
137(2)
References
139(4)
Robust regression with infinite moving average errors
143(16)
Patrick J. Farrell
Mohamedou Ould-Haye
1 Introduction
143(1)
2 S-estimators
144(1)
3 S-estimators' Asymptotic Behavior
145(5)
3.1 Weak Convergence of estimators
146(4)
4 Proof of Proposition 1
150(6)
5 Discussion
156(1)
References
156(3)
A note on the monitoring of changes in linear models with dependent errors
159(16)
Alexander Schmitz
Josef G. Steinebach
1 Introduction
159(1)
2 The testing procedure
160(3)
3 Examples
163(4)
3.1 Linear models with NED regressors
163(1)
3.2 Linear models with asymptotically M-dependent errors
164(1)
3.3 Monitoring strongly mixing AR models
165(2)
4 Proofs
167(6)
References
173(2)
Testing for homogeneity of variance in the wavelet domain
175
Olaf Kouamo
Eric Moulines
Francois Roueff
1 Introduction
176(2)
2 The wavelet transform of K-th order difference stationary processes
178(2)
3 Asymptotic distribution of the W2-CUSUM statistics
180(10)
3.1 The single-scale case
180(7)
3.2 The multiple-scale case
187(3)
4 Test statistics
190(2)
5 Power of the W2-CUSUM statistics
192(6)
5.1 Power of the test in single scale case
192(4)
5.2 Power of the test in multiple scales case
196(2)
6 Some examples
198(6)
References
204